Difference between revisions of "Manuals/calci/CHITEST"

From ZCubes Wiki
Jump to navigation Jump to search
Line 11: Line 11:
 
  Each cell has an expected frequency of at least five.
 
  Each cell has an expected frequency of at least five.
 
*The <math>\chi^2</math> test first calculates a <math>\chi^2</math> statistic using the formula:
 
*The <math>\chi^2</math> test first calculates a <math>\chi^2</math> statistic using the formula:
<math>\chi^2 = \sum_{i=1}^{columns}\sum_{j=1}^{rows}\frac{(observed ij-expected ij)^2}}{grand total}</math>
+
<math>\chi^2 = \sum_{i=1}^{columns}\sum_{j=1}^{rows}\frac{{observed ij-expected ij}^{2}}}{grand total}</math>
 
*observed ij is the array of the observed values in a given set of values
 
*observed ij is the array of the observed values in a given set of values
 
*expected ij = column i total*row j total/grand total  
 
*expected ij = column i total*row j total/grand total  

Revision as of 01:33, 25 November 2013

CHITEST(ar,er)


  • is the array of observed values
  • is the array of expected values

Description

  • This function gives the the value from the chi-squared distribution. i.e it calculates  statistic and degrees of freedom, then calls CHIDIST.

The conditions of test is

The table should be 2x2 or more than 2x2
Each observations should not be dependent
All expected values should be 10 or greater. 
Each cell has an expected frequency of at least five.
  • The test first calculates a statistic using the formula:

Failed to parse (syntax error): {\displaystyle \chi^2 = \sum_{i=1}^{columns}\sum_{j=1}^{rows}\frac{{observed ij-expected ij}^{2}}}{grand total}}

  • observed ij is the array of the observed values in a given set of values
  • expected ij = column i total*row j total/grand total
  • observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.
  • A low result of is an indicator of independence.
  • From the formula of we will get is always positive or 0.
  • 0 only if observed ij=expected ij for each i and j.
  • CHITEST uses the distribution with the number of Degrees of Freedom df.
where df=(r-1)(c-1),r>1 and c>1.
If r=1 and c>1, then df = c-1 or if r>1 and c=1, then df=r-1.
If r=c=1 then this function will give the error result


Column1 Column2 Column3 Column4
Row1 45 38 0.000313
Row2 10 23
Row3 12 26
Row4 40.5 49.36
Row5 19.56 16.44
Row6 17.05 17.41
Let’s see an example
B C
45 38
10 23
12 26
40.5 49.36
19.56 16.44
17.05 17.41
CHITEST (a, b)
i.e. =CHITEST (B2; C4, B5:C7) is 0.003